When giving fly casting lessons I often explain some of the terminology we instructors use so I figured it may help if I did a brief overview of some of my casting definitions. I'll add more as I think of them.
Cast - the act of lifting the fly or lure from the water and placing it back onto the water.
False cast - a cast where the line is kept in the air during repeated acceleration strokes
Acceleration stroke - The part of the cast when the rod is accelerating, and bending. The acceleration stroke ends with an abrupt stop.
Casting arc - the angle of the rod at the start and finish of the acceleration stroke.
Stroke length - the distance the rod handle (or your hand) moves during the acceleration stroke
Set down - gently lowering your rod tip back on the water.
Loop shape - the shape described by the fly line during the acceleration stroke (and set up in spey casts), a tight loop is when both legs (top and bottom) of the line are close together.
D loop - in roll casting and spey casting the shape the line describes as it hang behind you from the rod tip prior to the forward cast
Spey cast - a cast used to safely change direction
Anchor - in a roll or spey cast the anchor is the line that is laid out on the water prior to the forward delivery.
Anchor point - The point at which the line enters the water creating the anchor
Set up - in spey casting the repositioning of the line prior to the forward cast
Haul - where the line hand is used on either the back cast or forward cast to pull line through the rod guides, during the acceleration stroke, to increase line speed.
Double haul - when a haul is applied to both the back cast and forward cast prior to final delivery
Shooting line - when additional line is slipped into the cast at the end of the casting stroke to increase distance
Drift - repositioning of the rod back and up, at the end of the back casting stroke
Tracking - the need to keep your forward and back casts travelling in a straight line
I'll go into more detail on some of these definitions at a later date
Please let me know if you have more to add or if you want to comment on any of my definitions.